It's just a decent quality reverb (sounds to me more like a plate than hall), done subtlely. You should be able to do it with SF. Might try a few other 3rd party Dx or VST plugins (Sony's stock plugin doesn't give you a lot of options).

There are a few differences. In the reverb you are trying to achieve there is a long delay before the main reverb effect starts. The delay is around 600-700ms. Their reverb sounds like a hall emulation. The reverb either uses a LPF or naturally rolls off high end. I'd use a low pass filter at 6-12db per octave at about 5khz if your reverb is too bright.

Your reverb sounds like a plate with that washy decay. Yours also sounds mono and the original is quite stereo.

If I were setting this up and my reverbs weren't cutting it for me here is what I would try next.

Use an aux send on your audio track and put a delay on the aux. Set the delay to about 600-700ms and then fine tune the delay time to get you the delay. Set the feedback so you get one loud delay and then one or two quiet delays. Next put a stereo reverb on the delay track. Set the early reflection time to zero on the reverb. Add the LPF to the aux track either before or after the reverb and you are in business. This should get you closer so you can finish this up.

I don't have time right now to even test this out for you, so you'll have to go with some other suggestions (Paul999's sounds good).

What other thing you can do is this:
If, you have the ORIGINAL and you have the PROCESSED, you can DECONVOLVE the processed with the original to derive the convolution impulse response (which is basically the "thing that makes it sound like that"). You can take that and CONVOLVE another soundfile with it.

There are a few differences. In the reverb you are trying to achieve there is a long delay before the main reverb effect starts. The delay is around 600-700ms.

In Ozone Reverb I can't set the delay longer than 100ms so I will need another app.

Their reverb sounds like a hall emulation. The reverb either uses a LPF or naturally rolls off high end. I'd use a low pass filter at 6-12db per octave at about 5khz if your reverb is too bright.

I can't figure out whether its a plate or hall, plate is too metallic and hall is WAY too echoey especially on lower shelf.

Your reverb sounds like a plate with that washy decay. Yours also sounds mono and the original is quite stereo.

Yes, cornucopia advised to use plate and that did work out better than hall with the settings I've tried. I'm not sure if the original is really stereo. On the game the music is predominantly mono but I'll never know the exact source the author used and then reverbed, he could've remastered it into stereo.

Use an aux send on your audio track and put a delay on the aux.

Aux send? What program do you recommend?

@Cornucopia
I don't have the exact original. The output of the .gbs file has a louder upper shelf but I can fix this manually to match the equalizer of the reverbed. Should I still try the deconvolution? What program/plugin do you recommend? I haven't found too many deconvolvers.